There is no need to use a simplified or 'linear' leap-year correction calculation. For any algebraic Gregorian year value y the exact signed number of leap-year correction days in preceding years is easily calculated by the method of inclusions and exclusions. It is just

C(y) = 365(y - 1)
 + (y - 1)//4
 -  (y - 1)//100
 + (y - 1)//400

in which '//' denotes remainder-discarding binary-integer division.

John Gilmore
Ashland, MA 01721
USA

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